Re: Real mathematics vs FOL

biubo wrote:
"Nam Nguyen" <namducnguyen@xxxxxxx> wrote:
biubo wrote:
I have two questions:

1)Can you show me some mathematical results which cannot be translated into first order logic?

2) I remember that once I read on a book of Ebbinghaus, Flum, Thomas that in f.o. logic you can not define the concept of torsion group.
Is the theory of torsion groups out of the scope of FOL ?
It would be helpful if you could give some ideas as to what you
think "real mathematics" should be.

the common mathematics, the one that you can do without knowing much about logic.

OK. In that sense then I don't know much about 2) but regarding to
1), at least SR cannot be faithfully translated into FOL. (Think about
the impossibility of formalizing the relativity of events'
simultaneity.)





--
-----------------------------------------------------

What we call 'I' is just a swinging door which moves
when we inhale and exhale.
Shunryu Suzuki
----------------------------------------------------
.

Relevant Pages

  • Re: Questions on first vs second order logic
    ... > and thereby virtually all of mathematics. ... > So I guess the LUB theorem, written in SOL on most college textbooks, ... > both FOL and SOL formulations). ... Something similar occurs when one considers the first order theory RCF ...
    (sci.logic)
  • Questions on first vs second order logic
    ... and thereby virtually all of mathematics. ... quantification over individuals makes it difficult to use for the ... So I guess the LUB theorem, written in SOL on most college textbooks, ... both FOL and SOL formulations). ...
    (sci.logic)
  • Re: Can FOL formalize all of math?
    ... the notion of "covering" mathematics is pretty ... first-order logic corresponds to a theorem of FOL. ... the theorems of FOL do "cover" a lot of mathematics. ...
    (sci.logic)
  • Re: Real mathematics vs FOL
    ... biubo wrote: ... logic you can not define the concept of torsion group. ... think "real mathematics" should be. ... when we inhale and exhale. ...
    (sci.logic)
  • Re: Real mathematics vs FOL
    ... The Axiom of Separation in Z-F set theory cannot be expressed in FOL. ... logic you can not define the concept of torsion group. ... think "real mathematics" should be. ...
    (sci.logic)